Does the Copenhagen interpretation require the existence of God?

[Kuroneko]

The reason I mentioned quantum teleportation is that there is no classical, statistical analogue as far as I know. Can you explain to me how it works without quantum effects?

The issue wouldn't even come up. Quantum teleportation is the transfer of a quantum state. But in principle you can always copy a classical state. The quantum version is strictly weaker than the classical one here.

The reason I dislike the shoe analogy is that it makes it look like pure stats. Entanglement is not pure stats. It is a quantum state. Inside the box there would have to be half a left shoe, half a right shoe. I can manipulate these shoes to do all sorts of weird things that are not just down to stats.

Quantum mechanics is "stats". The rules of quantum probability are different from those of classical probability, but they are rules of probability all the same. That's precisely what a quantum state |ψ〉 is. For some observable A, if there is no degeneracy, it is completely determined by the wavefunction 〈A|ψ〉, which in turn is equivalent the probability density of measurement outcomes for that observable (the modulus-squared of the wavefunction) and the corresponding probability flux (the phase of the wavefunction, appropriately scaled).

The analogy seems to me quite good. With the probability↔quantum state identification in mind, entanglement is a very straightforward quantum translation of two particles having a joint probability distribution that is not independent.

[Alsor]

Entanglement is another name for the match (correlation) of certain parameters of different objects.

For example, when a bomb explodes and breaks into two parts, then we have:
Momentum: p1 + p2 = 0, the angular momentum L1 + L2 = 0;

Full compliance, a perfect correlation.

Then you can measure one and automatically get information about the state of the second (not necessarily complete).

[Grey]

It's worthwhile pointing out that quantum entanglement is more complicated than just the simple shoebox example presented. If it were just a matter of opening your box and thereby knowing what must be in the other one, it wouldn't be anything that anyone got excited about. In a past thread, Frog march suggested it was something similar:

As an example I thought it was like- a woman has three pairs of shoes, red,green and blue. She wears the red ones but packs her suitcase early in the morning with one of the other pairs, in the dark(so she doesn't wake her husband). She then gets on the plane in London and flys to NewYork perhaps you could say that the pair of shoes in the woman's suitcase and the pair she left back in London are entangled but neither she or her husband know what shoes are where. The husband comes home later that day and discovers the green shoes in the cupboard- the uncertainty has collapsed and he knows that when his wife opens her suitcase in NewYork she will find the blue shoes.

But quantum entanglement is a little bit more like this:

Let's revisit the woman and her shoes, with a slight change. Let's say she owns hundreds of pairs of shoes, all red, green, or blue, in equal proportion. She always packs one at random. If she does this many times, there will be a 1 in 3 chance for each color. Her husband always picks one of the boxes that she left behind at random and looks at the color. There's always a 1 in 3 chance for him to find each color. But, if they both open their boxes with them oriented the same way (either both vertically or both horizontally), there's a 1 in 2 chance that they picked the same color, whatever it was, while if they open their boxes holding them oriented differently, there's only a 1 in 6 chance that the colors match. The only way for that kind of correlation is if the act of opening the box is instantly communicated to the other pair of shoes somehow, and it has the possibility of changing its color in response. But also note that, since each measurement alone just gives a straight 1 in 3 chance for each color, just as we'd expect, there's no way to see this correlation, or to know which way the other person was holding the box (or even if they've opened it yet), until the woman comes back and they compare the results.

When you perform certain measurements on entangled particles, those measurements are correlated better than they "should" be, if you assume that the outcome of the measurement of particle A is independent of the type of measurement chosen to be made on particle B. But the details are always such that there's no way to determine which measurement choices were made on particle B just by looking at the results from particle A. It's only when you look at the correlations between the two that you find what Einstein would have called "spooky" results.

[Alsor]

You do not need here any action at a distance.
Just a little geometry ... spin is not the color - the distributions are different.

Simulation of EPR type correlations is very simple - just a few lines of code.

http://plato.stanford.edu/entries/bell-theorem/

Part 'Remote Context Independence' and:
(10) pm (s, t |a, b ) = p1m(s |a )p2m(t |b )

This is incorrect because it excludes the obvious correlation between the particles:
the spins are perfectly antiparallel, that is extremely correlated, not independent!

[utesfan100]

If the Copenhagen interpretation is wrong, can any conclusion one derives from it about God be a valid argument?

As a disclaimer, I believe in both God and Bohmian Mechanics. I cannot, however, prove either hypothesis relative to the corresponding null hypothesis. If hidden variables can't work, however, how does one explain this?

http://www.sciencemag.org/content/33.../1170.abstract

Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer

[Kuroneko]

It's worthwhile pointing out that quantum entanglement is more complicated than just the simple shoebox example presented. ...
But quantum entanglement is a little bit more like this: ...

You are correct that there are differences, but you are very mistaken in attributing this difference as fundamental to entanglement in the first place. The work horse in your example is that quantum probabilities interfere with one another, and the states form linear superpositions, unlike classical probabilities. But this is something intrinsic to all quantum probability whatsoever, from the simplest idealized single particles onwards.

It is completely accurate to say that entanglement is quantum-probabilistic correlation. If you look how entanglement is defined and declare "make all probabilities classical", you get classical correlation. And vice versa. They're direct analogues of one another, and the difference between them doesn't have anything to do with the entanglement, but everything to do with the difference between classical and quantum probabilities.

When you perform certain measurements on entangled particles, those measurements are correlated better than they "should" be, if you assume that the outcome of the measurement of particle A is independent of the type of measurement chosen to be made on particle B.

On the face of it, it's nonsensical: saying the particles are entangled is exactly the same statement as saying the measurement outcomes are correlated, for at least some observable. So of course if you assume that the outcomes of their measurements are independent for every observables ("what type...chosen"), you get into trouble--you're very explicitly making contradictory assumptions in your scenario.

I also don't understand what "correlated better" means. You can have 100% correlation in both, so there's doesn't seem to be any "better" or "worse" for either. On the other hand, if we're talking about all observables at once, then entanglement is strictly weaker than classical correlation (but again, this doesn't have anything fundamentally to do with entanglement, but the structure of quantum probabilities).

But the details are always such that there's no way to determine which measurement choices were made on particle B just by looking at the results from particle A. It's only when you look at the correlations between the two that you find what Einstein would have called "spooky" results.

It's only "spooky" if you take the Copenhagen interpretation and then insist that the wavefunction should be a real physical entity and its collapse therefore being "actual communication" of some sort. From the modern perspective, there's again little surprise about getting into trouble there: you're taking contradictory assumptions by insisting on something that Copenhagen denies. If you really want the state to do that, try a different interpretation.

[Grey]

So of course if you assume that the outcomes of their measurements are independent for every observables ("what type...chosen"), you get into trouble--you're very explicitly making contradictory assumptions in your scenario.

Well, sure, but that's why the result was surprising. in EPR, Einstein made the "reasonable" assumption that the result of a measurement of particle A could be considered completely independent from what direction an experimenter chose to measure the spin of particle B. It turned out that wasn't such a good assumption.

I also don't understand what "correlated better" means. You can have 100% correlation in both, so there's doesn't seem to be any "better" or "worse" for either. On the other hand, if we're talking about all observables at once, then entanglement is strictly weaker than classical correlation (but again, this doesn't have anything fundamentally to do with entanglement, but the structure of quantum probabilities).

If you make the assumption that the results of measurements on each particle are not affected by things that are happening arbitrarily far away, like which angle the other team sets their detector at (plus a few other assumptions, naturally, which seem pretty innocent, but who knows?), you can determine a limit of how well those results "should" be correlated, at best. That's Bell's inequality. And it turns out that for many choices of measurement, the correlation is better than that. In retrospect, it probably should have been almost obvious, since as you note, quantum probabilities have a phase associated with them and so the math isn't the same as when you're working with classical probabilities. Still, as far as I know, nobody prior to Bell had conclusively demonstrated that it was not possible to come up with some complicated local mechanism which could still explain the quantum facts.

It's only "spooky" if you take the Copenhagen interpretation and then insist that the wavefunction should be a real physical entity and its collapse therefore being "actual communication" of some sort. From the modern perspective, there's again little surprise about getting into trouble there: you're taking contradictory assumptions by insisting on something that Copenhagen denies. If you really want the state to do that, try a different interpretation.

Hence why "spooky" was in quotes: it was Einstein's term. He wanted to use an assumption of local realism to show that quantum mechanics had to be incomplete (though not incorrect). Instead Bell showed that no matter what you try to do, you have to abandon local realism. Einstein would have been profoundly unhappy with the result, I think.

[transreality]

Hence why "spooky" was in quotes: it was Einstein's term. He wanted to use an assumption of local realism to show that quantum mechanics had to be incomplete (though not incorrect). Instead Bell showed that no matter what you try to do, you have to abandon local realism. Einstein would have been profoundly unhappy with the result, I think.

Are you saying something along the lines of: say it is possible that the receiver of the shoe could be observing through a mirror that reverse the left/right identification of the object, and when the receiver communicates its observed identity he cannot be certain whether the shoe in the senders box is left or right, only that it would be the opposite of what he has seen locally, if he could observe it under the same local conditions. Or is that too trivial.

[Alsor]

Well, sure, but that's why the result was surprising. in EPR, Einstein made the "reasonable" assumption that the result of a measurement of particle A could be considered completely independent from what direction an experimenter chose to measure the spin of particle B. It turned out that wasn't such a good assumption.

Assumption is correct.
In this case the measurements are independent, but not results (because these are correlated, i.e. dependent).

Still, as far as I know, nobody prior to Bell had conclusively demonstrated that it was not possible to come up with some complicated local mechanism which could still explain the quantum facts.

Probability theory was built at the same time as the QM.
And even today there are a lot of paradoxes and misunderstandings in this area, especially with the conditional probability, which is directly related to the correlations.

Instead Bell showed that no matter what you try to do, you have to abandon local realism. Einstein would have been profoundly unhappy with the result, I think.

No. Bell made ​​a mistake in his calculations.

[Kuroneko]

Well, sure, but that's why the result was surprising. in EPR, Einstein made the "reasonable" assumption that the result of a measurement of particle A could be considered completely independent from what direction an experimenter chose to measure the spin of particle B.

I'm very uncertain as to how to interpret that. For example, what does 'considered' mean here?
1) If it means that team A's experimental results are predictable (in the probabilistic sense that all QM results are) by projecting the two-particle state to A's subspace and working with that, thus completely forgetting about what happens (or doesn't happen) to B, then it is definitely so. Taken in this near-literal manner, this is simply true in all possible interpretations of QM.
2) If it means that they are independent of the outcomes of measurements of B, then the situation is obviously self-contradictory in just the same way that "take a bachelor; assume he is married" is.
3) Something else?

If you make the assumption that the results of measurements on each particle are not affected by things that are happening arbitrarily far away, like which angle the other team sets their detector at (plus a few other assumptions, naturally, which seem pretty innocent, but who knows?), you can determine a limit of how well those results "should" be correlated, at best. That's Bell's inequality.

But they are not so affected. Einstein had a litmus test of 'reality': if you can in principle predict something with probability 1, it's definitely 'real'. What Bell showed is that the way this assumption gets you into trouble is in talking about the outcomes of experiments you haven't done.

To be more specific, the problem isn't found in comparing the result that team A got with the results team B got. You need to also compare the results team A got with "the results" team B would have gotten had their measuring apparatus had a different setting, even though there are no such results even in the gedankenexperiment. Without a move of this sort, the assumption of locality (that they don't affect one another) is completely consistent with QM.

And it turns out that for many choices of measurement, the correlation is better than that. In retrospect, it probably should have been almost obvious, since as you note, quantum probabilities have a phase associated with them and so the math isn't the same as when you're working with classical probabilities.

Ah, I see now what you meant. But note that for just as many, it's "worse", and the average difference over all settings is zero. So in a sense, it's just different rather than better or worse.

As an aside, to my knowledge, through path-integral formulation Feynman was the first to explicitly view quantum mechanics as a literal theory of probability in its own right that replaces classical probability theory. As contrasted with a new physical theory that replaces classical physics and happens to give out probabilities. This is a very natural move in hindsight, since wavefunction is equivalent to a probability density and a probability flux, but I've never heard it put neatly like that before reading Feynman & Hibbs.

No. Bell made ​​a mistake in his calculations.

Huh?

[Cougar]

Probability theory was built at the same time as the QM.
Bell made ​​a mistake in his calculations.

You seem to have some off-the-wall comments here, Alsor. What's the story?

[Strange]

Probability theory was built at the same time as the QM.

Surely it was developed by Pascal and Fermat in the 17th C?

[Alsor]

http://en.wikipedia.org/wiki/Conditional_probability

P(A and B) = P(A|B)*P(B);

Bell used:
P(A and B) = P(A) * P(B);

Thus, according to him: P(A) = P(A|B);
which means that he calculated the probability of two independent variables -
the two spins are random and independent, which means that they are antiparallel with probability p = 0, instead of p = 1.

http://en.wikipedia.org/wiki/Correla...sation_fallacy
It has not yet been discovered in QM, hence these paradoxes.

[Grey]

No. Bell made ​​a mistake in his calculations.

Since Bell's theorem is well-accepted by the physics community, I believe that a claim that it's wrong would more properly be handled under the rules of the AtM section, rather than diverting this thread. If you'd like to support such a claim, I encourage you to create such a thread, and I'll be happy to argue it with you there.

[Grey]

I'm very uncertain as to how to interpret that. For example, what does 'considered' mean here?

This is really pretty straightforward from reading the original EPR paper. Einstein felt that since you could make any measurement on one of a pair of entangled particles and the other one would have to give a matching result, and it was also clear (to him at least) that since particle A couldn't be affected by whatever measurement was actually performed by team B, particle A must "know in advance" how to respond to any possible measurement. That is, the last time particle A was affected in any way by particle B or what happens to it was when they were initially entangled, so all of particle A's potential responses to various choices of measurement must have been set at that time. To anthropomorphize the particles, it's like A and B each put together a list in a secret envelope: if I get measured at this angle, I'll give this result, if I get measured at this other angle, I'll give this other result, and they coordinate their lists so that they correlate appropriately. Since each particle actually had definite outcomes set for all the various measurement possibilities, but quantum theory only give a probabilistic prediction of how they will behave, quantum theory must be incomplete (although, since it's probabilistic predictions are correct, statistically, quantum theory is not incorrect). Einstein felt that, in principle at least, there could be some deeper theory that could account for the observed behavior, but which would be based on these deterministic elements of reality that quantum theory overlooks. I think it's pretty well accepted that Einstein was wrong about this. That is, Bell's theorem shows that you simply cannot create such a list in advance for particles A and B, unless you also know in advance which measurements will actually be performed. The only way such a hidden variables model can work is if you allow the lists to change on the fly (well, see below for one of the other ways out of this bind), based on what happens arbitrarily far away, which I think would have made Einstein very unhappy.

But they are not so affected. Einstein had a litmus test of 'reality': if you can in principle predict something with probability 1, it's definitely 'real'. What Bell showed is that the way this assumption gets you into trouble is in talking about the outcomes of experiments you haven't done.

To be more specific, the problem isn't found in comparing the result that team A got with the results team B got. You need to also compare the results team A got with "the results" team B would have gotten had their measuring apparatus had a different setting, even though there are no such results even in the gedankenexperiment. Without a move of this sort, the assumption of locality (that they don't affect one another) is completely consistent with QM.

Absolutely. I'd alluded to that when I mentioned "other assumptions", most of which are pretty hard to deny (like assuming that the basic rules of logical inference are valid), but this is one of the big ones, usually termed contrafactual definiteness. We do this all the time in our everyday lives, assuming that if we had chosen to act differently, we can surmise what the result would have been, and that it's meaningful to talk about such (like "Wow, if I hadn't hit the brakes in time, I would have slammed right into that other car!", or "If I hadn't stayed up so late watching that movie, I wouldn't be so tired this morning.") If you deny contrafactual definiteness, and insist that it's not meaningful to talk about the results we might have gotten from hypothetical measurements, it's not even possible to formulate Bell's theorem. It's a perfectly valid stance to take; a little odd perhaps, since we accept contrafactual statements so easily in normal life, but certainly there are plenty of things that we take for granted in our everyday lives that are not really true.

[Alsor]

Since Bell's theorem is well-accepted by the physics community, I believe that a claim that it's wrong would more properly be handled under the rules of the AtM section, rather than diverting this thread. If you'd like to support such a claim, I encourage you to create such a thread, and I'll be happy to argue it with you there.

What are you talking about?
Simply upload the correlated data to two remote computers, where you calculate what you want - locally, and Bell's theorem falls immediately.

These are the basics of probability theory, nothing more.

Students produce a variety of stupidity on exercises - Bell's Theorem is no exception.

[pzkpfw]

What are you talking about?

He's talking about accepted physics. If you wish to argue this further, start an ATM thread (assuming you've not already had one on this subject). No more in this thread.

[Alsor]

The main stream is a Mathematical Science - formal, strict and unambiguous, and not some naive interpretations, resulting from insufficient recognition of the problem.


P (A and B) = P (A | B) * P (B);

So in the case of EPR for polarizers, we have:
A - photon passed through the first polarizer, B - by the second:

P (B) = 1/2, and P (A) = 1/2;
This is standard - photons are random.

but they are maximally correlated, so the conditional:

P (A | B) = cos(a-b)^2; a, b - the angles of the polarizers

And finally:
P (A and B) = 1/2 * cos(a-b)^2;
Similarly:
P (~ A and ~ B) = 1/2 * cos(ab)^2, because it is symmetrical.

consistent results: cos(a-b)^2
other cases: sin(a-b)^2;
correlation: cos(a-b)^2 - sin(a-b)^2 = cos(2*(a-b));

This is a good problem to exercise at school - for children.
Good luck in discovering the foundations of probability theory.

[Argos]

Swap "observation" for "interaction" and all the problem goes away...

[Alsor]

Swap "observation" for "interaction" and all the problem goes away...

You talk about the mechanism of realization the observed results?

This is a different matter.
Statistics does not depend on the method of realization/implementation - it did not give the causes of the observed results at all.

[Argos]

I was responding to this passage on the opening post:

According to the Copenhagen interpretation of quantum mechanics, no one event can have occurred until it is observed. But obviously we stand at the end of a 13.4 billion-year chain of quantum events; a universe-full of them, in fact. So who was doing the observing?

No one was 'observing', but particles were interacting among themselves. A sentient observer is not required.

[pzkpfw]

...

"No more" means no more.

[kevin1981]

I was responding to this passage on the opening post:

According to the Copenhagen interpretation of quantum mechanics, no one event can have occurred until it is observed. But obviously we stand at the end of a 13.4 billion-year chain of quantum events; a universe-full of them, in fact. So who was doing the observing?

No one was 'observing', but particles were interacting among themselves. A sentient observer is not required.

That is what i said at post 12.

I thought the wave function state only applied to individual particles when separated from the outside
environment. So there is no need for consciousness, as when particles interact with each other that collapses the wave function.
Particles certainly interacted before consciousness evolved.

So is what i said right. I just want to know if what i have learnt is correct.

[Squink]

If there were a proof of the existence of God within quantum mechanics, the Jesuits would have found it years ago, and they'd have told us all about it.

They've certainly tried to find it: Patrick Heelan - Quantum Relativity and the Cosmic Observer etc. etc.

So, where is it?

[swampyankee]

Really. Not a thread about religion per se, just puzzled. According to the Copenhagen interpretation of quantum mechanics, no one event can have occurred until it is observed. But obviously we stand at the end of a 13.4 billion-year chain of quantum events; a universe-full of them, in fact. So who was doing the observing? Any entity with the capacity to observe all quantum events in the history of the universe would have to be a) immortal b) omnicient and c) omnipresent. Bar omnipotence and such a being begins to look a lot like a deity.

I think it's just as logically supportable to conclude that the Copenhagen interpretation forbids the existence of God. Science, in my opinion, cannot really be used to provide evidence for either the presence or absence of God.

[tnjrp]

It is very difficult to use science to provide evidence for actual nonexistence of something, especially something as abstract and nebulous as divinity. Even a specific deity that has been philosophized to bitz (most obvious example being Christian God) is in practice disprovable. At best you can get by with "absence of evidence is very weak evidence of abscence".

But indeed the general consensus among scientists (who are of course by and large godless heathens ) looks to be that no consciousness, immortal, mortal, omniscient or rudimentary is required to interpret quantum physics. Of course there are notable exceptions to this rule, not all of the Xtian (IIRC).

[profloater]

It is very difficult to use science to provide evidence for actual nonexistence of something, especially something as abstract and nebulous as divinity. Even a specific deity that has been philosophized to bitz (most obvious example being Christian God) is in practice disprovable. At best you can get by with "absence of evidence is very weak evidence of abscence".

But indeed the general consensus among scientists (who are of course by and large godless heathens ) looks to be that no consciousness, immortal, mortal, omniscient or rudimentary is required to interpret quantum physics. Of course there are notable exceptions to this rule, not all of the Xtian (IIRC).

At least Maxwell's thought experiment about his demon ruled out demons.

[swampyankee]

At least Maxwell's thought experiment about his demon ruled out demons.

...or at least the chance of finding one to run an air conditioner.